To calculate the shear viscosity, we perturb the background metric by \( h^{y}_{x} \) . We call the perturbed part of metric \(\psi =h^{y}_{x}\)  [1]}, [2]}.
\(ds^{2} =-N^2\tilde{H} dt^{2} +\frac{ dz^2 }{u^2\tilde{H}} +\frac{ z^2}{u^2 l^2}\Bigg ( \sum _{i=1}^{D-2}dx_i^2+2\psi (t,\vec{x},z)dx_1dx_2\Bigg ),\) 
